🧮 algebra

1. **State the problem:** A packet of crayons and an exercise book together cost 2.70. A packet of crayons costs 1.25.

1. Let's start with a simple algebra problem: Solve for $x$ in the equation $2x + 5 = 15$. 2. The formula to solve for $x$ is to isolate $x$ on one side of the equation. We do this

1. Berilgan ifoda: $$\frac{\left(\frac{1}{a} + \frac{1}{b} - \frac{c}{ab}\right)(a + b + c)}{\frac{1}{a^2} + \frac{1}{b^2} + \frac{2}{5}ab - \frac{c^2}{a^2b^2}}$$ 2. Qiymatlarni qo

1. The problem is to solve the equation without using the dollar sign symbol. 2. Since no specific equation is given, let's clarify that in math, the dollar sign is not used in equ

1. **State the problem:** We have the quadratic equation $$x^2 + kx + 15 - k = 0$$ and need to find the values of $$k$$ such that it has two distinct real roots. 2. **Formula and r

1. Diberikan persamaan $$\sqrt{1 + \log_3 x^5 + \sqrt{1 + \log_3 x^5 + \sqrt{1 + \log_3 x^5 + \cdots}}} = 3$$. Kita diminta mencari nilai dari $$\log_3 x^{81}$$. 2. Misalkan $$y =

1. **Problem 1.16:** Calculate $ (6\sqrt{5} + 2\sqrt{3}) \times 9\sqrt{5} $. 2. **Formula and rules:** Use distributive property: $ (a+b)c = ac + bc $. Also, $ \sqrt{a} \times \sqr

1. **Problem:** Simplify the expression $5\sqrt{7} \times (3\sqrt{2} + 7\sqrt{7})$. 2. **Formula and rules:**

1. **Planteamiento del problema:** Tenemos la función lineal $$f(x) = 5x + 6$$ y debemos resolver varias preguntas relacionadas con esta función. 2. **Fórmula general de funciones

1. The problem is to deduce a property or value graphically from the function $f$. 2. To solve this, we first need the explicit form of the function $f(x)$ or its graph.

1. Diberikan pertidaksamaan: $$3(2x-2) \leq 2x + 9$$ 2. Gunakan sifat distribusi untuk menghilangkan tanda kurung:

1. Diberikan persamaan \(7^{x^2 - x - 1} = 3^{x+1}\). Kita diminta mencari nilai \(x_1 + x_2\) dimana \(x_1\) dan \(x_2\) adalah akar-akar persamaan tersebut. 2. Langkah pertama ad

1. **State the problem:** Simplify the expression $$\frac{x^5-25x^3}{x^5-3x^4-10x^3} - \frac{\frac{x^3-5x^2-6x}{x^2-4x-12}}{\frac{x^2-2x-8}{x^2-x-12}}$$

1. The problem asks for the domain of the function $$f(x) = \frac{7 - 3x}{4x - 9}$$. 2. The domain of a rational function is all real numbers except where the denominator is zero b

1. **Problem:** Evaluate the function $f(x)=2x+1$ at several inputs. 2. **Formula used:** For any input $x$, substitute it into $f(x)=2x+1$ and simplify.

1. **State the problem:** Solve the equation $$-5.1 = 3x + 2.4$$ for $$x$$. 2. **Isolate the variable term:** Subtract 2.4 from both sides to get the term with $$x$$ alone.

1. **State the problem:** Solve the equation $$x + \frac{1}{3} = \frac{4}{3}$$. 2. **Formula and rules:** To solve for $x$, we need to isolate $x$ on one side of the equation. This

1. **State the problem:** We want to find all integers $n$ such that $$(n + 3)(n - 7) \leq 0.$$ 2. **Understand the inequality:** The product of two factors is less than or equal t

1. **State the problem:** We are given two equations: $$9s + 5t = 108$$ and $$s = t - 2$$. We need to find the value of $$t$$. 2. **Use substitution:** Since $$s = t - 2$$, substit

1. The problem asks if the equation $6x - 11 = -72$ correctly represents "Six times the difference of 11 and a number is -72."\n\n2. Recall the phrase "difference of 11 and a numbe

1. The problem states: "Six times the difference of 11 and a number is -72." We need to write this as an equation using $x$ to represent the number. 2. The phrase "the difference o